Mysql - I'm trying to resolve mysql query. I think it can be done via sbquery

Question

Have a tbl simiar to the following

 col1 col2 col3 col4
  a    b    a
  a    b1   a2   x
  a    b13  a21   x
  b    1b    1a
  b    1b1  a21  v
  b    1b11  a21  v1

...

I'm trying to figure out how to do a query that triggers off of col3 'limit 1' for each group of col1

doing

select * from tblX where col3='a21' limit 1 

obviously doesn't work

however,

 select * from tblX where col3='a21' and col1='a' limit 1 

and

 select * from tblX where col3='a21' and col1='b' limit 1 

would ... but this being multiple operations..

Any pointers on creating a single query?

thanks obviously doesn't